Chapter 7, Solution 1C.

Transcription

1 hapter 7, Solutio 1. he velocity of the fluid relative to the immered olid body ufficietly far away from a body i called the free-tream velocity,. he uptream or approach velocity i the velocity of the approachig fluid far ahead of the body. hee two velocitie are equal if the flow i uiform ad the body i mall relative to the cale of the free-tream flow. hapter 7, Solutio. body i aid to be treamlied if a cociou effort i made to alig it hape with the aticipated treamlie i the flow. Otherwie, a body ted to bloc the flow, ad i aid to be blut. tei ball i a blut body ule the velocity i very low ad we have creepig flow. hapter 7, Solutio 3. he force a flowig fluid exert o a body i the flow directio i called drag. rag i caued by frictio betwee the fluid ad the olid urface, ad the preure differece betwee the frot ad bac of the body. We try to miimize drag i order to reduce fuel coumptio i vehicle, improve afety ad durability of tructure ubjected to high wid, ad to reduce oie ad vibratio. hapter 7, Solutio 4. he force a flowig fluid exert o a body i the ormal directio to flow that ted to move the body i that directio i called lift. It i caued by the compoet of the preure ad wall hear force i the ormal directio to flow. he wall hear alo cotribute to lift ule the body i very lim, but it cotributio i uually mall. hapter 7, Solutio 5. Whe the drag force, the uptream velocity, ad the fluid deity ρ are meaured durig flow over a body, the drag coefficiet ca be determied from 1 ρ where i ordiarily the frotal area the area projected o a plae ormal to the directio of flow of the body. hapter 7, Solutio 6.

2 he frotal area of a body i the area ee by a pero whe looig from uptream. he frotal area i appropriate to ue i drag ad lift calculatio for blut bodie uch a car, cylider, ad phere. hapter 7, Solutio 7. he part of drag that i due directly to wall hear tre τ w i called the i frictio drag, frictio ice it i caued by frictioal effect, ad the part that i due directly to preure P ad deped trogly o the hape of the body i called the preure drag, preure. or leder bodie uch a airfoil, the frictio drag i uually more igificat. hapter 7, Solutio 8. he frictio drag coefficiet i idepedet of urface roughe i lamiar flow, but i a trog fuctio of urface roughe i turbulet flow due to urface roughe elemet protrudig further ito the highly vicou lamiar ublayer. hapter 7, Solutio 9. a reult of treamliig, a frictio drag icreae, b preure drag decreae, ad c total drag decreae at high Reyold umber the geeral cae, but icreae at very low Reyold umber ice the frictio drag domiate at low Reyold umber. hapter 7, Solutio. t ufficietly high velocitie, the fluid tream detache itelf from the urface of the body. hi i called eparatio. It i caued by a fluid flowig over a curved urface at a high velocity or techically, by advere preure gradiet. Separatio icreae the drag coefficiet dratically. hapter 7, Solutio 11. he frictio coefficiet repreet the reitace to fluid flow over a flat plate. It i proportioal to the drag force actig o the plate. he drag coefficiet for a flat urface i equivalet to the mea frictio coefficiet. hapter 7, Solutio 1.

3 he frictio ad the heat trafer coefficiet chage with poitio i lamiar flow over a flat plate. hapter 7, Solutio 13. he average frictio ad heat trafer coefficiet i flow over a flat plate are determied by itegratig the local frictio ad heat trafer coefficiet over the etire plate, ad the dividig them by the legth of the plate. hapter 7, Solutio 0. ir flow over the top ad bottom urface of a thi, quare plate. he flow regime ad the total heat trafer rate are to be determied ad the average gradiet of the velocity ad temperature at the urface are to be etimated. umptio 1 Steady operatig coditio exit. he critical Reyold umber i Re cr Radiatio effect are egligible. Propertie he propertie of air at the film temperature of + / 54+/ 3 are able -15 ρ g/m c p 07 J/g W/m Pr alyi a he Reyold umber i L 60 m/0.5 m 6 Re L m / which i greater tha the critical Reyold umber. hu we have turbulet flow at the ed of the plate. m / ir 60 m/ L b We ue modified Reyold aalogy to determie the heat trafer coefficiet ad the rate of heat trafer τ 1.5 N 0.5 m 3 N/m f τ 0.5ρ 3 N/m g/m 60 m/ f / 3 Nu L / 3 Nu St Pr Pr Re L Pr Re L Pr L 1/ 3 1/ 3 f 6 1/ Nu Re L Pr W/m. h Nu W/m. L 0.5 m Q h 6.6 W/m. [ 0.5 m ] W

4 c umig a uiform ditributio of heat trafer ad drag parameter over the plate, the average gradiet of the velocity ad temperature at the urface are determied to be u u τ 3 N/m τ μ ρ g/m 1.67 h 0 0 h 5 m / W/m W/m 5 /m hapter 7, Solutio 30E. refrigeratio truc i travelig at 55 mph. he average temperature of the outer urface of the refrigeratio compartmet of the truc i to be determied. umptio 1 Steady operatig coditio exit. he critical Reyold umber i Re cr Radiatio effect are egligible. 4 ir i a ideal ga with cotat propertie. 5 he local atmopheric preure i 1 atm. Propertie umig the film temperature to be approximately 80, the propertie of air at thi temperature ad 1 atm are able -15E Btu/h.ft Pr ft / ir 55 mph 80 Refrigeratio truc L 0 ft alyi he Reyold umber i L [55 580/3600 ft/]0 ft 6 Re L ft / We aume the air flow over the etire outer urface to be turbulet. herefore uig the proper relatio i turbulet flow for Nuelt umber, the average heat trafer coefficiet i determied to be hl 0.8 1/ / 3 Nu Re L Pr Btu/h.ft. 4 h Nu Btu/h.ft. L 0 ft Sice the refrigeratio ytem i operated at half the capacity, we will tae half of the heat removal rate Btu/h Q 18,000 Btu/h he total heat trafer urface area ad the average urface temperature of the refrigeratio compartmet of the truc are determied from [0 ft9 ft + 0 ft8ft + 9 ft8ft ] 84 ft 4

5 Q h Q h 18,000 Btu/h Btu/h.ft. 84 ft 77.7 hapter 7, Solutio 39. or the lamiar flow, the heat trafer coefficiet will be the highet at the tagatio poit which correpod to θ 0. I turbulet flow, o the other had, it will be highet whe θ i betwee 90 ad. hapter 7, Solutio 40. urbulece move the fluid eparatio poit further bac o the rear of the body, reducig the ize of the wae, ad thu the magitude of the preure drag which i the domiat mode of drag. a reult, the drag coefficiet uddely drop. I geeral, turbulece icreae the drag coefficiet for flat urface, but the drag coefficiet uually remai cotat at high Reyold umber whe the flow i turbulet. hapter 7, Solutio 41. rictio drag i due to the hear tre at the urface wherea the preure drag i due to the preure differetial betwee the frot ad bac ide of the body whe a wae i formed i the rear. hapter 7, Solutio 4. low eparatio i flow over a cylider i delayed i turbulet flow becaue of the extra mixig due to radom fluctuatio ad the travere motio. hapter 7, Solutio 50. he flow of a fluid acro a iothermal cylider i coidered. he chage i the drag force ad the rate of heat trafer whe the free-tream velocity of the fluid i doubled i to be determied. alyi he drag force o a cylider i give by ρ 1 N Whe the free-tream velocity of the fluid i doubled, the drag force become ir Pipe

6 N ρ aig the ratio of them yield 4 1 he rate of heat trafer betwee the fluid ad the cylider i give by Newto' law of coolig. We aume the Nuelt umber i proportioal to the th power of the Reyold umber with 0.33 < < he, Re 1 Nu h Q Whe the free-tream velocity of the fluid i doubled, the heat trafer rate become Q aig the ratio of them yield Q Q 1